It is the same concept as that the height is determined from how effective you are at converting kinetic energy from the run into potential energy at the max height. However the argument will always be, how much more energy can your body create through the swing. And for the tuck and shooters of the world, how much energy they can put into the pole with their own muscles.

I do believe the swing coverts run energy the most effective because it is the most natural motion and requires the least amount of human interaction to deviate from the natural motion.

Just on the case of the dirt bike jump, you will also notice that it is not just the speed of approach causing height. As to get a little extra pop, riders will sit down at the very end sometimes to compress the suspension to cause a little more upward motion of the bike before it leaves the end of the ramp, also known as 'seat bouncing'.